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κ = 1.017889833900852e-3: two full rank-two entrances with complete prefix replay - #421

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eumemic:codex/e8-capacity217-target-prefixes
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eumemic:codex/e8-capacity217-target-prefixes

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@eumemic eumemic commented Oct 11, 2026

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κ = 1.017889833900852e-3

Exact conditional κ: 254472458475213 / 250000000000000000. This improves frozen #420 by 77197194607 / 1000000000000000000 > 0. This is a new branch and new PR; prior published heads and claims remain frozen.

Concurrent #418 reports κ = 0.001017923290728024 and #419 reports κ = 0.001017962405296845, both numerically higher. Their current descriptions retain changed-phase and complete assembly or invoice obligations. This PR supplies a complete changed-composition replay improving #420 under the explicit broader chronological/dyadic conditions; it is not advertised as the highest current numerical claim or as acceptance by unchanged legacy gx/gxcore.

Two helpers acquire full rank-two entrances: helper 435 in [304,111] through helper421 += helper435, and helper 367 in [259,246] through helper257 += helper367. Exact frame propagation admits the new spaces and adds five frame changes relative to the 215-gauge predecessor. Every original A scalar instruction stays fixed. The complete word has 217 gauges, 377 entrance dimensions, 701 entrance instructions and ten changed original-A frames. The constructor checks all 1,021 full-word and retained-snapshot columns against the predecessor composed with the literal shears.

The final word rebuilds #404's target 124/125 chronological recovery, #376's frame edit, #402's target 177/220 resynthesis and the target 124/144 prefixes on the actual changed source. Its 6,996 nongauged response entries and 7,097 signed unit response macros are freshly recomputed. The local verifier checks both actual scalar orientations, arbitrary dirty restoration, private erasure, both reflected scalar/frame ledgers, the exact chronological target bracket and 16 literal coefficient-word microchecks. Quarter/eighth coefficients are lowered through paid copy, halving, accumulation and clearing primitives. All ten reverted-frame controls and the new omitted-entrance control reject; every chronological entrance omission witness is checked.

Sixty-four replicas and 576 complete invocations use 5,871 width-73 banks per stage and 2,855 rank-one pads, with live stock 114,279 and physical stock 115,070. The profile has 2,581,407 paid children, rank mass 8,322,399 and deficit 19,968. The complete owner/schedule/adapter routes and both paid profiles are rebuilt and independently decoded. All 249,984 explicit bank-boundary adapters are charged. The invoice counts 66,178,176 real scalar primitives, local bound 9,499,228,707,576 and row 15,451 < 20,161. All 876 new/reflected Gaussian phase pairs, 45 residual charts and 23,040 address columns pass, together with six response controls, 13 bank controls, the reserve bridge, two rational moment engines and all 47 strict outer inequalities.

python -B research/e8-capacity217-target-prefixes/verify.py /absolute/path/to/new/output

The development replay and clean committed Git archive replay passed before publication; every staged package blob matched its manifest. Python 3.11+ and C++17 are required. Dedicated Linux CI covers Python 3.11 and 3.14. Default verification reuses pinned evidence for the unchanged bit component and old local phase edges; --replay-bit freshly repeats the bundled bit component. Reused checks are not represented as newly executed. Exact complex coarse lower: 1018926989324773613017 / 1000000000000000000000000; unchanged bit lower: 255384852701747 / 250000000000000000.

This is a finite conditional construction. All-size compressed-window, arbitrary-correlated dirty-bank, recursive compiler, ordinary-call/fixed-tape/restored-row, common-grid, precision and analytic interfaces remain inherited assumptions. The chronological target and dyadic conditions extend the older sufficient guards: no unchanged legacy gx/gxcore E4/E5 acceptance, Lean certificate or unconditional multiplication theorem is claimed.

Provenance: frozen #420 (079d514cdb40b2152ffa743853556b0117b98438), #416, #414, #411, #410 and #408; Dugongue #404 (12f488264cdd74a3b60d0fb534f4955792384f5c); Chafik Boukhalfa/Anthropic Claude #402 (7883c63ec724999b921c2304b66648cbb9e7a112); applecrusher #376; Rohan Arun #409 as grouped-entrance search inspiration; and the retained E8, bit, compiler and analytic lineage. #412/#413/#415/#418/#419 were read as comparison claims; no implementation was imported from them. The two rank-two entrances, propagated frames, exact prefix relocation, full bank assembly and audits were prepared for eumemic with substantial OpenAI Codex assistance. Original licenses, notices and AI disclosures are preserved.

@Mister-Meeseeks

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Thank you @eumemic. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Two full rank-two entrance spaces.

Review and limits: Complete native finite contract including chronological propagation and charged dyadic prefixes. It remains conditional on the stated global/all-size interfaces.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: 6dfe3f978e2fcf3701523bda73744d56a1f8ac6f. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.

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